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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2010 Volume 7, Pages C.258–C.282 (Mi semr287)

This article is cited in 9 papers

Proceedings of conferences

$r$-pseudoinverse for a compact operator

V. A. Tcheverda, V. I. Kostin

Institute of Geophysics SB RAS, Novosibirsk, Russia

Abstract: The notion of a generalized $r$-solution for a system of linear algebraic equations is modified for approximation of the generalized inverse for a compact linear operator from a separable Hilbert space $X$ into a separable Hilbert space $Y$. Approximation of the $r$-pseudoinverse by projection method is proposed and justified. Stability of the results with respect to data perturbations and approximation error of the operator is analyzed.

Keywords: compact operator, singular value decomposition, projection method, $r$-pseudoinverse.

UDC: 519.676

MSC: 47A52

Received February 2, 2010



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